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arXiv 2411.02001cs.LGcs.NE
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无限宽度下的局部损失优化:预测编码网络与目标传播的稳定参数化

Local Loss Optimization in the Infinite Width: Stable Parameterization of Predictive Coding Networks and Target Propagation

Science Tokyo(东京科学大学);AIST(国家信息与通信技术研究所)

Satoki Ishikawa, Rio Yokota, Ryo Karakida

AI总结:

该研究针对局部学习算法难稳定调参的问题,为预测编码和目标传播引入无限宽度下的最大更新参数化,验证了超参数跨宽度迁移性,并揭示了其区别于反向传播的独特性质。

摘要:

局部学习通过逐层局部目标与损失训练网络,一直被视作神经计算中反向传播(BP)的替代方案。然而,受局部性限制,这类算法往往更复杂,或需要额外超参数,导致难以确定能让算法稳定推进的理想设置。为提供理论与定量层面的洞见,我们针对两种代表性的局部目标设计——预测编码(PC)和目标传播(TP),引入了无限宽度极限下的最大更新参数化($μ$P)。我们验证了$μ$P可实现不同宽度模型间的超参数迁移。此外,分析还揭示了$μ$P具备传统BP所没有的独特且有趣的性质。通过分析深度线性网络,我们发现PC的梯度会在一阶梯度与类高斯-牛顿梯度之间插值,具体取决于参数化方式。我们证明,在特定标准设置下,无限宽度极限中的PC表现更接近一阶梯度。对于TP,即便采用与经典$μ$P不同的末层标准缩放方式,其局部损失优化也更偏向特征学习机制而非核机制。

英文摘要:

Local learning, which trains a network through layer-wise local targets and losses, has been studied as an alternative to backpropagation (BP) in neural computation. However, its algorithms often become more complex or require additional hyperparameters because of the locality, making it challenging to identify desirable settings in which the algorithm progresses in a stable manner. To provide theoretical and quantitative insights, we introduce the maximal update parameterization ($μ$P) in the infinite-width limit for two representative designs of local targets: predictive coding (PC) and target propagation (TP). We verified that $μ$P enables hyperparameter transfer across models of different widths. Furthermore, our analysis revealed unique and intriguing properties of $μ$P that are not present in conventional BP. By analyzing deep linear networks, we found that PC's gradients interpolate between first-order and Gauss-Newton-like gradients, depending on the parameterization. We demonstrate that, in specific standard settings, PC in the infinite-width limit behaves more similarly to the first-order gradient. For TP, even with the standard scaling of the last layer, which differs from classical $μ$P, its local loss optimization favors the feature learning regime over the kernel regime.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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